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CSE 326: Data Structures Lecture #7 Branching Out
... refs (&) coming. You can do all of this without refs... just watch out for special ...
... refs (&) coming. You can do all of this without refs... just watch out for special ...
Question Bank - Saraswathi Velu College of Engineering
... For any node n, the depth of n is the length of the unique path from the root to node n. Thus for a root the depth is always zero. 4. What is the length of the path in a tree? The length of the path is the number of edges on the path. In a tree there is exactly one path form the root to each node. 5 ...
... For any node n, the depth of n is the length of the unique path from the root to node n. Thus for a root the depth is always zero. 4. What is the length of the path in a tree? The length of the path is the number of edges on the path. In a tree there is exactly one path form the root to each node. 5 ...
Data Structure and Algorithms
... The ‘pivotal value’(or the ‘Height factor’) is greater than 1 or less than–1. ...
... The ‘pivotal value’(or the ‘Height factor’) is greater than 1 or less than–1. ...
COMP 261 Lecture 14
... • DFS of the graph, set node count number • For each node, split other nodes into – Subtree nodes – Non-subtree nodes ...
... • DFS of the graph, set node count number • For each node, split other nodes into – Subtree nodes – Non-subtree nodes ...
Data Structures for Midterm 2
... General insert is O(n) due to shifting data O(1) lookup if index is known O(n) find – O(log(n)) if sorted using binary search ...
... General insert is O(n) due to shifting data O(1) lookup if index is known O(n) find – O(log(n)) if sorted using binary search ...
Heaps - WordPress.com
... There are two main uses of heaps. The first is as a way of implementing a special kind of queue, called a priority queue. Recall that in an ordinary queue, elements are added at one end of the queue and removed from the other end, so that the elements are removed in the same order they are added (FI ...
... There are two main uses of heaps. The first is as a way of implementing a special kind of queue, called a priority queue. Recall that in an ordinary queue, elements are added at one end of the queue and removed from the other end, so that the elements are removed in the same order they are added (FI ...
Data Structures
... • For non-empty binary tree whose nonterminal nodes (i.e., a full binary tree) have exactly two nonempty children: #of leaves = 1+#nonterminal nodes • In a Drozdek-complete tree: # of nodes = 2height-1; one way to see this is to use the statement #of leaves = 1+#nonterminal nodes; another way is to ...
... • For non-empty binary tree whose nonterminal nodes (i.e., a full binary tree) have exactly two nonempty children: #of leaves = 1+#nonterminal nodes • In a Drozdek-complete tree: # of nodes = 2height-1; one way to see this is to use the statement #of leaves = 1+#nonterminal nodes; another way is to ...
Self-balancing Binary Search Trees
... 1. Each node is either red or black. 2. The root is black. 3. The leaves are all NULL pointers and they are black. 4. If a node is red, then both its children are black. 5. Every path from a given node to any of its descendant NULL nodes contains the same number of black nodes. From 4 and 5 we can i ...
... 1. Each node is either red or black. 2. The root is black. 3. The leaves are all NULL pointers and they are black. 4. If a node is red, then both its children are black. 5. Every path from a given node to any of its descendant NULL nodes contains the same number of black nodes. From 4 and 5 we can i ...
Data Structure Review
... If a node has no parent (there will be exactly one of these), then it is the root of the tree. ...
... If a node has no parent (there will be exactly one of these), then it is the root of the tree. ...
(6-up)
... • Recursive methods can be wri_en to operate on trees in an obvious way • Base case – empty tree – leaf node ...
... • Recursive methods can be wri_en to operate on trees in an obvious way • Base case – empty tree – leaf node ...
Trees
... rightChild(v): Return the right child of v; an error condition occurs if v is an external node. ...
... rightChild(v): Return the right child of v; an error condition occurs if v is an external node. ...
Computer Science Foundation Exam
... 1) (10 points) Order Notation Assume that the operations below are implemented as efficiently as possible. Using Big-O notation, indicate the time complexity in terms of the appropriate variables for each of the following operations: a) Popping every element off a stack containing n elements b) Add ...
... 1) (10 points) Order Notation Assume that the operations below are implemented as efficiently as possible. Using Big-O notation, indicate the time complexity in terms of the appropriate variables for each of the following operations: a) Popping every element off a stack containing n elements b) Add ...
IT4105-Part1
... If one visit the nodes of this tree using a preorder traversal, in what order will the nodes be ...
... If one visit the nodes of this tree using a preorder traversal, in what order will the nodes be ...
Complete Binary Trees
... be the continental divide. So the surveyers started at Yellowstone Park, mapping out the border, but at “Lost Trail Pass” they made a mistake and took a false divide. They continued along the false divide for several hundred miles until they crossed over a ridge and saw the Clark Fork River cutting ...
... be the continental divide. So the surveyers started at Yellowstone Park, mapping out the border, but at “Lost Trail Pass” they made a mistake and took a false divide. They continued along the false divide for several hundred miles until they crossed over a ridge and saw the Clark Fork River cutting ...
Data Structure
... two single linked lists into one list, Reversing a single linked list, applications of single linked list to represent polynomial expressions and sparse matrix manipulation, Advantages and disadvantages of single linked list, Circular linked list, Double linked list UNIT V: Trees: Basic tree concept ...
... two single linked lists into one list, Reversing a single linked list, applications of single linked list to represent polynomial expressions and sparse matrix manipulation, Advantages and disadvantages of single linked list, Circular linked list, Double linked list UNIT V: Trees: Basic tree concept ...
Slides
... Suffix Trees • Given a string s, a suffix tree for s is a tree such that – each edge has a unique label, which is a non-null substring of s – any two edges out of the same node have labels beginning with different characters – the labels along any path from the root to a leaf concatenate together t ...
... Suffix Trees • Given a string s, a suffix tree for s is a tree such that – each edge has a unique label, which is a non-null substring of s – any two edges out of the same node have labels beginning with different characters – the labels along any path from the root to a leaf concatenate together t ...
Dynamic Order Statistics More Data structure ???? Isn`t it an
... First Try: Each key stores its rank. So we only need to find the key (takes O(log n) in most data structures) and retrieve the rank. So OS-Rank(x, S) takes O(log n) ...
... First Try: Each key stores its rank. So we only need to find the key (takes O(log n) in most data structures) and retrieve the rank. So OS-Rank(x, S) takes O(log n) ...
Trees
... These have many applications, some of which we will discuss. The most obvious is storing hierarchical structures, such as genealogies, file structures, and organizational structures. The root (which corresponds to a single data element) is at the top, and the branches are arranged below the root and ...
... These have many applications, some of which we will discuss. The most obvious is storing hierarchical structures, such as genealogies, file structures, and organizational structures. The root (which corresponds to a single data element) is at the top, and the branches are arranged below the root and ...
x - Yimg
... For n = 0 T (n) = (c + d)n + c (c + d) . 0 + c = c = T (0). For n > 0, T (n) = T (k) + T (n − k − 1) + d = ((c + d)k + c) + ((c + d)(n − k − 1) + c) + d = (c + d)n + c − (c + d) + c + d = (c + d)n + c , which completes the proof. ...
... For n = 0 T (n) = (c + d)n + c (c + d) . 0 + c = c = T (0). For n > 0, T (n) = T (k) + T (n − k − 1) + d = ((c + d)k + c) + ((c + d)(n − k − 1) + c) + d = (c + d)n + c − (c + d) + c + d = (c + d)n + c , which completes the proof. ...
Trees, Binary search trees
... – there is one visit at the root, and – one visit for every edge in the tree – since every node but the root has exactly one parent, and the root has none, must be N − 1 edges in any non-empty tree. ...
... – there is one visit at the root, and – one visit for every edge in the tree – since every node but the root has exactly one parent, and the root has none, must be N − 1 edges in any non-empty tree. ...
document
... Each node of the tree is at a specific level or depth within the tree The level of a node is the length of the path from the root to the node This pathlength is determined by counting the number of links that must be followed to get from the root to the node The root is considered to be level ...
... Each node of the tree is at a specific level or depth within the tree The level of a node is the length of the path from the root to the node This pathlength is determined by counting the number of links that must be followed to get from the root to the node The root is considered to be level ...
Dictionary ADT and Binary Search Trees
... first, then process left child, then process right child. • Post-Order Traversal: Process left child, then process right child, then process data at the node. • In-Order Traversal: Process left child, then process data at the node, then process right child. Who cares? These are the most common ways ...
... first, then process left child, then process right child. • Post-Order Traversal: Process left child, then process right child, then process data at the node. • In-Order Traversal: Process left child, then process data at the node, then process right child. Who cares? These are the most common ways ...
Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a (non-empty) binary tree is a triple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. Some authors allow the binary tree to be the empty set as well.From a graph theory perspective, binary (and K-ary) trees as defined here are actually arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which actually appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. A binary tree is a special case of an ordered K-ary tree, where k is 2.In computing, binary trees are seldom used solely for their structure. Much more typical is to define a labeling function on the nodes, which associates some value to each node. Binary trees labelled this way are used to implement binary search trees and binary heaps, and are used for efficient searching and sorting. The designation of non-root nodes as left or right child even when there is only one child present matters in some of these applications, in particular it is significant in binary search trees. In mathematics, what is termed binary tree can vary significantly from author to author. Some use the definition commonly used in computer science, but others define it as every non-leaf having exactly two children and don't necessarily order (as left/right) the children either.